Can neuroevolution be combined with gradient descent?
The paper The Comparison and Combination of Genetic and Gradient Descent Learning in Recurrent Neural Networks: An Application to Speech Phoneme Classification (2007), by Rohitash Chandra and Christian W. Omlin, uses genetic algorithms to train a recurrent neural network and then uses gradient descent to fine tune the trained model.

The paper Evolutionary Stochastic Gradient Descent for Optimization of Deep Neural Networks (2018), by Xiaodong Cui, Wei Zhang, Zoltán Tüske and Michael Picheny, also combines evolutionary algorithms and gradient descent, but, in this case, they alternate between a gradient descent step and an evolution step. This is an example of a evolutionary stochastic gradient descent (ESGD) method, as opposed to a population-based training (PBT) method, which uses only evolutionary algorithms to train neural networks.